Field measurements for the validation of antennas are, in current practice,
obtained in the near-field region (nearer to the antenna than where the
ultimate angular intensity pattern is apparent) to improve measurement quality
and reduce cost. The large-scale linear transformation between the near-field
and far-field patterns is typically accomplished using the fast Fourier
transform (FFT). The restriction the FFT places on the measurement locations
(to a regular planar grid), however, is often not realized in practice. As
measurement frequencies increase and mobile measurement platforms with less
stable scanners are increasingly employed, this problem becomes more severe.

This project was formed with the goal of creating a practical, accurate method
for computing the near-field to far-field transformation for data taken at
non-ideal measurement locations. The investigators have designed and
implemented an algorithm that meets this goal. It combines the
recently-developed nonequispaced fast Fourier transform, interpolation, and
conjugate gradient iteration to achieve any prescribed accuracy in nearly
optimal computational complexity. The method requires order
operations per iteration, where n is the number of measurements; in current
practice, n is typically between and .

This work has generated interest among researchers working with other
measurements, including plane polar data, and further work will address
mathematical issues that arise in related application areas.